Most widely used conventional hot water supplies of this kind have therein one electric heater heated by controllable electric current is. See for example, U.S. Pat. No. 4,461,949, which discloses an electrically controllable electric heater in the boiler. Since such hot water supply systems must heat the whole water in the tanks by single heater, they have disadvantages that the heaters must have large heating values and that they take long time to heat the water even to a lower preset temperature, yet consuming large amount of electric energy. There have been, therefore, proposed improvements in supplying hot water economically with less electric powder. For example, Japanese Utility Model Publication No. 49(1974)-39965 discloses a storage-type hot water supply system having a main heater that utilizes night-time electric power and a sub-heater that utilizes daytime electric power. The system stores at a predetermined temperature the hot water heated by the main heater at night and heats the water fed into the tank during daytime by means of the latter heater. With this constitution, it is possible to prevent lowering of the temperature of the water in the tank after if is used and fed with new water, utilizing ecomomic night electricity to boil the water to minimize the heating cost. Yet, this hot water supply is incapable of adjusting itself to varying conditions such as the consumption rate of the hot water and ambient temperature. Since the consumption of the hot water varies from time to time in a day, it is desirable from a point of convenient utilization of economic night electricity to have the heating value (calorific value) increased during the hours of large consumption but decreased during the hours of low consumption. Further, it is most desirable to have a minimum calorific value sufficient to prevent the water from freezing during winter night when ambient temperature is lower and no hot water is used, as well as during a long non-using period, for example vacation. Thus, the control of electric heating for a hot water supply system that can meet the varying conditions of consumption and temperature will be needed for effective and convenient hot water supply, which have not been realized yet so far in prior art including the aforementioned publication and other U.S. patents.